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Mathematics Mapping For Instruction Kindergarten Prince William County Public Schools June 2003 (Updated July 2005) MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 PRINCE WILLIAM COUNTY SCHOOLS Kindergarten Mathematics Curriculum Map The kindergarten standards place emphasis on developing the concept of number by counting; combining, sorting, and comparing sets of objects; recognizing and describing simple repeating patterns; and recognizing shapes and sizes of figures and objects. Students will investigate nonstandard measurement, collect data, and create graphs. While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies such as calculators and computers. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative concepts and relationships or for proficiency in basic computations. Mathematics has its own language, and the acquisition of specialized vocabulary and language patterns is crucial to a student’s understanding and appreciation of the subject. Students should be encouraged to use correctly the concepts, skills, symbols, and vocabulary identified in the following set of standards. Problem solving is the cornerstone of the mathematics curriculum. It is the central focus of the mathematics curriculum and provides the context in which concepts and skills can be learned. Mathematical understanding develops from problem situations that have meaning to children and are related to their environment and experiences. Classrooms with a problem-solving basis are filled with thought-provoking questions, speculations, investigations, and explorations. Students learn that mathematics should and does make sense. Solutions should be explained and shared enabling students to see that problems may be solved in more than one way. A major goal of problem-solving instruction is to enable students to develop strategies to solve problems. Strategies include but are not limited to using manipulatives, making an organized list or table, using trial and error, drawing a diagram, looking for a pattern, and acting out a problem. Problem solving steps should include Polya’s four-step framework for problem solving: 1. Understand the problem, 2. Devise a plan or decide on an approach for attacking the problem, 3. Carry out the plan, 4. Look back at the problem, the answer, and what you have done to get there. Steps are not to be taught, rather they are used as an organizer for instruction and planning. Problem solving has been integrated throughout the six content strands. The development of problem solving skills should be a major goal of the mathematics program at every grade level. Students must be helped to develop a wide range of skills and strategies for solving a variety of problem types. Situations allowing students to experience problems will better prepare them to be problem solvers in their daily lives. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Sample Assessment Techniques Category Technique Information Provided Observations Anecdotal Records immediate evaluation and feedback of learning, focus on specific learner expectations, social Conferences skills and behaviors, teamwork, interactions, knowledge into context, levels of Checklists understanding, relationships, attitude, oral language skills, listening skills, analysis, real-life application, process, procedures, equipment handling Journals Journal understanding, written ability, conventions, organizations, pre and post comparisons, Personal Response Journal feedback to teachers, personal connections, social skills, connection to concepts in literature, Dialogue Journals understanding of story elements, internalization of literature, personal experience, goal Reflective Interactive On-line Journals setting, understanding process, affective mode, background knowledge Tests and Quizzes Multiple Choice Paper and Pencil pre and post test of knowledge, content mastery, ability to make inferences, recall, True/False Matching recognition, memorization, content, problem solving process, summative information Short Answer Extended Response Performance Tasks Simulations Multimedia Productions creativity, understanding, end product, public speaking and performing, group work, Demonstrations Presentations organization skills, application of skills to new situations, reasoning skills, analysis, real-life Lab Experiments Software Demonstrations application, process, procedures, equipment handling Investigations Data Analysis Mathematical Models Written Projects Laboratory Reports Research Papers logical organization, hypothesis, comprehension, following directions, writing skills, use of Essays Brochures logic, interpersonal relations, expression, vocabulary, style, understanding of different Interactive Notes writing structures/genres, research skills, evaluations, summative, initiative Oral Projects Retelling Questions/Responses comprehension, synthesis, paraphrasing, speaking and listening skills, substantiation of Debates Audio Tapes positions, development of counter argument, reasoning, assessment of background Interviewing Teaching a Lesson knowledge, perspective, organization, decision making skills, personal information, attitude, synthesizing, analyzing, memorization, interpretation, composure, confidence Visual Projects Story Boards Collages/Maps/Designs assessment of background knowledge, comprehension, organization, creativity, growth and Illustrations Photographs maturity level, depth of conceptualization, good for non-readers or early readers, application, Advertisements Models synthesis, process, application of knowledge and skills, equipment use, decision making Multimedia Projects Scrapbooks Science Fair Displays Work Samples Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense mathematical communication, mathematical When are sets equal? reasoning, connections, and representation SOL Reporting Category to: Number and Number Sense When does one set have fewer items than another set? Match each member of one set with members of another set, using the concept Concept When does one set have more items than another set? of 1-to-1 correspondence to compare the Comparing Sets of Items number of members between sets, where What do the terms fewer, more, and the same mean? each set contains 10 or fewer items. PWC Grade Level Objective K.1 Compare and describe two sets of 10 or K.1A The student will model sets Critical Attributes fewer items using the terms more, fewer, containing ten or fewer concrete items. A set is a collection of distinct elements or items. and the same. K.1B The student will identify and describe one set as having more, fewer, A one-to-one correspondence exists when two sets have an equal number of items. Essential Understanding or the same number of members as the All students should: other set, using the concept of one-to- Strategies for developing the concept of one-to-one matching involve set comparisons Understand how quantities relate to each one correspondence. without counting. Hands-on experiences in matching items between two sets into 1-to- other, which leads to an understanding of 1 correspondence by moving, touching, and aligning objects enables visual as well as how numbers are related to each other. Virginia SOL K.1 kinesthetic comparisons of the number of items in the two sets. The student, given two sets containing 10 or fewer concrete items, will identify Students can also use the strategy of counting to make comparisons between two sets and describe one set as having more, without matching the sets, using one-to-one correspondence. fewer, or the same number of members as the other set, using the concept of one-to-one correspondence. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Student will construct two sets, then describe one set as more, less, or the same. PWC Math Web Page: Number and Number Sense http://www.pwcsmath.com Students are paired boy-to-girl, etc. Each pair of students holds hands. Next, the Curriculum and Evaluation Standards, SOL Reporting Category teacher will ask: "Is there anyone left over? Which is less? More? Same?‖ NCTM, 1989 Number and Number Sense Principals and Standards for School Student takes a handful of unifix cubes (i.e., two colors) from a grab bag. The Mathematics, NCTM, 2000 Concept cubes of each color are snapped together. The group compares them to see which NCTM Addenda Series – Kindergarten Comparing Sets of Items color is more and which is less or if they are the same. Math Their Way. Investigations in Number, Data, and Space, PWC Grade Level Objective K.1 Mathematical Thinking in Kindergarten, Virginia SOL K.1 Investigation 1, Investigation 4 Developing Number Concepts: Counting Comparing and Pattern Chapter 3 Counting and Numbers - Windows of Mathematics, Creative Publications NCTM Addenda Series - Kindergarten Nimble with Numbers, ―Show Them Change,‖ ―Three in a Row,‖ ―Capture Two‖ The M & M Counting Book by Barbara Barbieri McGrath Fish Eyes by Lois Ehlert Anno's Counting Book by M. Anno Teddy Bear's One to Ten by Suzanne Gretz AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Matching Tops and Bottoms,‖ AIMS Magazine, Volume 10 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense What are number words? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How do the number words relate to counting? to: Number and Number Sense Count orally the number of items in a set of Critical Attributes concrete items containing ten or fewer Concept There are three developmental levels of counting: items, using one-to-one correspondence, Counting Items in a Set of Ten or Less 1. Rote sequence and identify the corresponding numeral. 2. One-to-one correspondence Identify written numerals 0 - 10 presented PWC Grade Level Objective K.2 3. The cardinality of numbers in random order. K.2A The student will count the number Counting involves two separate skills: verbalizing the standard list of the natural Select the numeral from a given set that of items in a set of ten or fewer concrete number words in order – ―one, two, three,..‖ and connecting this sequence in one-to- corresponds to a set of 10 or fewer concrete items. one correspondence with the items in the set being counted. items. K.2B The student will select a Write the numerals 0 - 10. corresponding numeral from a given set With oral repetition and practice, students learn names and sequence of numbers. Write a numeral that corresponds to a set of of 10 or fewer after counting the number When the oral sequence of numbers has been mastered, student will begin to manually ten or fewer concrete items. of items. count numbers. K.2C The student will write the numeral Essential Understanding to tell how many are in a set of 10 or Association of number words with collections of objects is achieved by moving, All students should: fewer after counting the number of touching, or pointing to objects as the number words are spoken. Objects may be Read and write numerals 0 - 10. items. presented in random order or arranged for easy counting. Numbers are related to Understand that the total number of objects specific amounts. In counting a set, the last number named represents not only the last can be found by counting. Virginia SOL K.2 object named but also the total number of objects in the collection. This is referred to The student, given a set containing ten or as the cardinality of the set (cardinal numbers). Counting objects in different order fewer concrete items, will does not alter the result. a) tell how many are in the set by counting the number of items orally; Kinesthetic involvement, or tracing the numbers using tactile materials, e.g., sand, b) select the corresponding numeral sandpaper, carpeting, or finger paint, facilitates the writing of numerals. from a given set; and c) write the numeral to tell how many Articulating the characteristics of each numeral when writing numbers has been found are in the set. to reduce the amount of time it takes to learn to write numbers. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Numeral Recognition Strategies: PWC Math Web Page: Number and Number Sense Provide student with a variety of counting experiences (i.e., books, songs, finger http://www.pwcsmath.com plays). Curriculum and Evaluation Standards, SOL Reporting Category NCTM, 1989 Number and Number Sense Spray shaving cream in a small pile on the table. Each student spreads out cream Principals and Standards for School and writes numerals. Mathematics, NCTM, 2000 Concept NCTM Addenda Series – Kindergarten Counting The teacher marks containers with the numbers 0 - 9. Students count out the Early Childhood Math, ECM, Books corresponding number of objects and place it in the appropriate container. 5 and 8. PWC Grade Level Objective K.2 Math Their Way. Virginia SOL K.2 Children will work in pairs with one child displaying a set of cubes numbered Investigations in Number, Data, and Space, from 1 - 10 and the other child sounding their instrument an equal number of Mathematical Thinking in Kindergarten, times. Investigation 1 Developing Number Concepts: Counting Allow each child to trace a hand on art paper. Write the child's name on the hand Comparing and Pattern Chapter 1 and cut it out. Make a bulletin board with an envelope at the bottom; place the cut Nimble with Numbers Action Counting out hands inside the envelope. Tack nine index cards on the bulletin board, Connect to the NCTM Standards p. 16-36 number 0 - 9. Staple loops of yarn on the bulletin board. Tack some "hands" The M & M Counting book by Barbara inside each loop. Allow students to tack the number in loop that tells how many Barbieri McGrath hands. Then students can trace numeral with their finger. Fish Eyes by Lois Ehlert Teddy Bear's One to Ten by Suzanne Gretz AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense How do we know if the object is first, second, third, fourth, or fifth? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How do we know where to begin counting? to: Number and Number Sense Identify the ordinal positions first, second, Critical Attributes third, fourth and fifth using ordered sets of Concept Understanding the cardinal and ordinal meaning of numbers is necessary to quantify, five concrete objects and/or pictures of Order and Compare measure, and identify the order of objects. such sets presented from:: Left-to-right PWC Grade Level Objective K.3 An ordinal number is a number that names the place or position of an object in Right-to-left K.3A The student will use ordinal sequence or set, e.g., first, third. Ordered position, ordinal position, and ordinality are Top-to-bottom numbers in sequencing an ordered set of terms that refer to the place or position of an object in a sequence or a set. Bottom-to-top five objects or pictures and indicate the ordinal position of each item. The ordinal position is determined by where you start in an ordered set of objects or Essential Understanding K.3B The student will identify and sequence of objects. All students should: demonstrate the meaning of ordinal Use ordinal numbers to describe the order positional terms from left-to-right, right- The ordinal meaning of numbers is developed by identifying and verbalizing the place of items in a sequence. to-left, top-to-bottom, and/or bottom-to- or position of objects in a set or sequence, e.g., the student’s position in line when top. students are lined up alphabetically by their first name. Virginia SOL K.3 Ordinal numbers identify the position of an object from a given starting point. The student, given an ordered set of Progression may be from left to right, right to left, top to bottom, or bottom to top. three objects and/or pictures, will indicate the ordered position of each The starting point would be the first object in the sequence. item, from left-to-right, right-to-left, top- to-bottom, and/or bottom-to-top. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Make a stick of unifix cubes putting specific colors first, second, third, fourth, and PWC Math Web Page: Number and Number Sense fifth. http://www.pwcsmath.com Curriculum and Evaluation Standards, SOL Reporting Category Students line up first through fifth from different starting positions. NCTM, 1989 Number and Number Sense Principals and Standards for School Make a train from three shoeboxes by painting one as the engine, one as a boxcar, Mathematics, NCTM, 2000 Concept and one as the caboose. The teacher emphasizes that the engine is always first and NCTM Addenda Series – Kindergarten Order and Compare the caboose is always last. Students will identify familiar objects as being in the Early Childhood Math, ECM first, second, or third box. Math Their Way PWC Grade Level Objective K.3 Pancakes Pancakes by Eric Carle Virginia SOL K.3 AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Pockets,‖ AIMS Magazine, Volume 10 Issue 2, May 1997, p 3 ―Let Me Count the Ways,‖ Primarily Bears, Book 1 ―A Bear Eggspedition,‖ AIMS Magazine, Volume 7 Issue 9 ―Mighty Mittens,‖ Glide Into Winter Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense What is a pattern? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How is a pattern identified, created, and extended? to: Number and Number Sense Group 30 or fewer objects together into sets What pattern is formed when counting by five? Ten? of fives or tens, and then count them by Concept fives or by tens. Counting Critical Attributes Investigate and recognize the pattern of The patterns developed as a result of skip-counting are precursors for recognizing counting by fives and tens, using 30 or PWC Grade Level Objective K.4 numeric patterns, functional relationships, and concepts underlying money, telling fewer concrete objects. K.4A The student will group objects into time, and multiplication. Powerful models for developing these concepts include Investigate and recognize the pattern of sets of fives and tens. counters, hundreds boards/charts, and calculators. counting by fives and tens to 30, using a K.4B The student will recognize patterns calculator. from counting by fives and tens to thirty Skip counting by fives lays the foundation for reading a clock effectively, telling time using concrete objects, instructional to the nearest five minutes, and counting money, as well as developing the Essential Understanding aides and calculators. multiplication facts for five. All students should: Understand that skip counting can be used Virginia SOL K.4 Skip counting by tens is a precursor for place value, addition, counting money, and to count a collection of objects. The student will investigate and multiplying by multiples of ten. Describe patterns in skip counting and use recognize patterns from counting by those patterns to predict the next number or fives and tens to thirty, using concrete Calculators can be used to display visually the numeric patterns that result from skip numbers in the skip counting sequence. objects and a calculator. counting. Use the constant feature of the four-function calculator to display the numbers in the sequence when skip counting by that constant, e.g., skip counting by fives, press 5 + 5 = = = … to produce 5, 10, 15... Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Using adding machine tape taped above the chalkboard, write a number daily for PWC Math Web Page: Number and Number Sense each day in school. Use a different color to show multiples of five, and a http://www.pwcsmath.com box/circle around the number to show multiples of ten. Count daily by ones, Curriculum and Evaluation Standards, SOL Reporting Category fives, and/or tens. NCTM, 1989 Number and Number Sense Principals and Standards for School Use counters, group them into groups of five or ten; then count them. Mathematics, NCTM, 2000 Concept NCTM Addenda Series – Kindergarten Counting Use several tens frames to count by ten, or five frames to count by fives. Early Childhood Math, ECM, Book 7 Math Their Way PWC Grade Level Objective K.4 Using nickels the child will determine how many groups of five (nickels) are NCTM Addenda Series - Kindergarten. Virginia SOL K.4 needed to get to 50. Developing Number Concepts: Counting Comparing and Pattern Chapter 2 Using a sentence strip, make a number line with 5, 10, 15, etc. missing. Students Two, Four, Six, Eight (A Book About fill in the missing numbers. Legs) by Ethel and Leonard Kessler. The Most Amazing Hide and Seek Sing along with tape recordings that count by fives and tens. Counting Book by Robert Crowther Connect to the NCTM Standards, p 36 Students will work in pairs. One student punches in a 5 on the calculator and the other child colors in the 5 square on a 100’s chart. Each time 5 is punched on the AIMS Activities: calculator; the appropriate square is colored on the chart. Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Pumpkin Cover-up,‖ AIMS Magazine, Volume 8 Issue 3 ―A Jar That Likes to Keep You Guessing,‖ Primarily Bears, Book 1 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense How is counting to 30 by ones done? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How is counting backward (twenty to zero) done? to: Number and Number Sense Count forward from 1 to 30. What is the number before and after a given number? Count backward from 20 to 1. Concept Counting Critical Attributes Essential Understanding Numerals are abstract representations of objects. Our number system is based on ten, All students should: PWC Grade Level Objective K.5 using the digits 0 – 9. These digits are then assigned a place, giving the digit value, Use the correct oral counting sequence in K.5A The student will count forward to with 0 as a placeholder. Numbers can be counted forward or backward in consecutive both forward and backward counting thirty. order. situations. K.5B The student will count backward from twenty. Counting skills are essential components of the development of number ideas; however, they are only one of the indicators of the understanding of numbers. Virginia SOL K.5 The student will count forward to 30 and Counting forward by rote memorization advances the child’s development of backward from 10. sequencing. Students should count the natural numbers, 1, 2, 3, 4, … These are not to be confused with the whole numbers that begin with the integer zero. Counting backward by rote memorization lays the foundation for subtraction. Students should count backward beginning with 10, 9, 8, … through… 3, 2, 1. Counting forward and backward can lead to the development of counting on and counting back. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Calendar Activities: PWC Math Web Page: Number and Number Sense Straw count - Add 1 straw each day (school). Total number of days should be the http://www.pwcsmath.com same as the numeral written on the number line that day. The class counts the Curriculum and Evaluation Standards, SOL Reporting Category straws. When there are "ten" straws, wrap them with a rubber band and move then NCTM, 1989 Number and Number Sense to a "tens" box. Principals and Standards for School Mathematics, NCTM, 2000 Concept Number Line - Each day record the number of days the class has attended school NCTM Addenda Series – Kindergarten Counting that year. Numbers that are multiples of ten are written in a different color. Later Early Childhood Math, ECM, Book 1 in year underline multiples of fives. Use questions to get student responses: ex- Math Their Way PWC Grade Level Objective K.5 How many days have we been in school this year? NCTM Addenda Series, Kindergarten. Virginia SOL K.5 Number Sense Numbers on a line, p 51 Keep a tally count of the days for the month. Developing Number Concepts: Counting Comparing and Pattern Chapter 1 Play, "I'm thinking of a number". Give clues and student uses the calendar to help Too Many Monkeys figure out number. There Were Ten in the Bed by Pam Adams Hand Rhymes by Mark Brown Children will practice counting with songs, rhymes, and finger plays such as "Ten Finger Plays: Five Little Monkeys, Ten Little Indians: or "Five Little Pumpkins". Counting backwards or forwards may Little Indians be used to time clean ups. Records: Math Readiness Count Up - Count Down by Hap Palmer Play Blast-Off. Students squat down and count slowly from 10-0. Jump up when reaching zero. AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―You Can Count on Us,‖ Fall Into Math and Science ―Apples A Peel to ME,‖ Fall Into Math and Science ―Home Free,‖ Sense-able Science ―Feet Findings,‖ Spring Into Math and Science Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Computation and Estimation How are two sets combined to equal sums 1 – 10? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How are sets separated? to: Computation and Estimation Combine two sets (knowing the number in When is it appropriate to combine or separate sets when shown the symbols each set), and count the combined set to Concept + or -? determine the sum, where the sum is not Addition and Subtraction of Whole greater than 10 concrete items. Numbers Critical Attributes Remove, ―take away,‖ or separate part of a Sums and differences can be shown using various manipulatives, including pennies. set from a given set to determine the result PWC Grade Level Objective K.6 The processes of addition and subtraction can be demonstrated by combining and of subtraction. K.6A The student will add whole separating sets. numbers using up to ten concrete items. Essential Understanding Use manipulatives to identify and Whole numbers are 0, 1, 2, 3, 4, 5, 6, and so on. All students should: demonstrate various combinations of Understand addition joins items together numbers with sums up to ten. Addition is the process of combining or joining sets. and subtraction separates items out. K.6B The student will subtract whole numbers using up to ten concrete items. Subtraction can be viewed through a ―take away‖ or ―separate‖ interpretation or as the Use manipulatives to represent the difference between two sets. process of subtraction. Counting on from the larger set to determine the sum of the combined sets is a strategy Virginia SOL K.6 for finding a sum. The student will add and subtract whole numbers using up to ten concrete items. Counting backward from the larger set to determine the difference between two sets is a strategy for subtraction. Students should ―compose‖ and ―decompose‖ numbers (i.e., 9 is 5 and 4) to begin to develop proficiency with number facts. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Use counters to represent children in the pool altogether. Two children and one PWC Math Web Page: Computation and Estimation child is three children. There are three children altogether. Repeat. Use more http://www.pwcsmath.com counters to represent more children. Curriculum and Evaluation Standards, SOL Reporting Category NCTM, 1989 Computation and Estimation Display two apple trees on a bulletin board, with approximately ten, moveable Principals and Standards for School apples. Use the apples to show a displayed addition number sentence. Show Mathematics, NCTM, 2000 Concept apples fallen from the tree to make a subtraction number sentence. NCTM Addenda Series – Kindergarten Addition and Subtraction of Whole Early Childhood Math, ECM, Book 8 Numbers Groups of students stand up and act out an oral word problem. Choose physical Math Their Way attributes, such as, short sleeves, long sleeves and the teacher will ask, "How Math Their way Summary Newsletter. PWC Grade Level Objective K.6 many are wearing long sleeves? ... How many are wearing short sleeves? … How NCTM Addenda Series, Kindergarten. Virginia SOL K.6 many are there all together? …Those with long sleeves sit down. … How many Peter and the Penny Tree are left?" Twenty Six Letters and Ninety-Nine Cents by Tana Holban I went to the Market by Joseph Domjan There Was an Old Lady Who Swallowed a Fly by Pam Adams Big Addition Book by Becky Daniel Developing Number Concepts Addition and Subtraction Navigating Through Algebra Chapters 2, 3 The Doorbell Rings by Pat Hutchins Annie's Pet by Barbara Brenner Finger Plays: Five Little Monkeys AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Quick Quilts Part 1 and 2,‖ AIMS Magazine, Volume 7 Issue 8 ―Pig's Tale,‖ AIMS Magazine, Volume 7 Issue 10 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Number and Number Sense How is a whole object divided into two equal parts (halves)? mathematical communication, mathematical reasoning, connections, and representation to: SOL Reporting Category What is a fraction? Demonstrate the part to whole concept of Number Sense one half Critical Attributes Represent a whole to show it having two Concept Students use concrete objects to show the part-to whole concept and the part-part- equal parts: Fractions/Decimals whole concept. o Region/area models, e.g., pie pieces o Measurement models, e.g., PWC Grade Level Objective K.19 Cutting a cookie into halves represents the part-to-whole concept. Groups of objects Cuisenaire rods, connecting cubes. The student will use concrete can be divided into two equal parts to show the part-to-whole relationship using objects to show the part to whole halves. concept using halves. All students should A set of two green balls and two blue balls in a box represents the part-part-whole Understand that a fraction represents a part NO SOL concept. Two and two are parts and four is the whole. Emphasis is placed on the parts of a whole. of a whole and not on the memorization of fraction notation. Understand that fractional parts are equal shares of a whole. Understand that the fraction name (half) tells the number of equal parts of things that are being counted. Understand that the top number (numerator) names the number of parts being counted. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Tell a story about sharing a cookie between two people. Discuss how that would PWC Math Web Page: Number and Number Sense be done. http://www.pwcsmath.com Curriculum and Evaluation Standards, SOL Reporting Category Divide the students in class in half for various activities. Half the students stand NCTM, 1989 Number Sense on one side of the room, half on the other side. Principals and Standards for School Mathematics, NCTM, 2000 Concept Students make a stick of Unifix cubes. Make half one color and the other half a NCTM Addenda Series – Kindergarten Fraction/Decimals different color. Early Childhood Math, ECM, Book 7 Math Their Way PWC Grade Level Objective K.19 NO SOL AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Measurement Name each coin and tell its value. mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category What is the value of a collection of coins? to: Computation and Estimation Describe the properties/characteristics (e.g., Critical Attributes color, relative size) of a penny, nickel, Concept Involvement in varied activities such as physically manipulating coins and making dime, and quarter. Money comparisons about their size, color, and value is prerequisite to this skill. Identify a penny, nickel, dime, and quarter. Count a randomly placed collection of PWC Grade Level Objective K.7 Counting money helps students gain an awareness of consumer skills and the use of pennies and/or nickels or models of pennies K.7A The student will identify and money in everyday life. and/or nickels, and determine its value up recognize a penny, nickel, dime, and to ten cents. quarter. A variety of classroom experiences in which students manipulate physical models of K.7B The student will determine the money and count forward to determine the value of a collection of coins are important Essential Understanding value of a collection of pennies, and /or activities to ensure competence with money. All students should: nickels up to ten cents. Develop common reference for identifying Establishing a one-to-one correspondence between the number names and the items in pennies, nickels, dimes, and quarters. Virginia SOL K.7 the set is essential for an accurate count. Understand the value of a collection of The student will recognize a penny, coins whose value is 10 cents or less. nickel, dime, and quarter and will determine the value of a collection of pennies, and/or nickels whose total value is ten cents or less. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Use objects in the room, and teacher-made price tags to display a "store". PWC Math Web Page: Measurement Children use real or model pennies to "purchase" objects. http://www.pwcsmath.com Curriculum and Evaluation Standards, SOL Reporting Category A penny a day can be earned as a reward to be spent at a teacher-made store. NCTM, 1989 Computation and Estimation Principals and Standards for School Start a penny jar. Save for classroom project. Have students count the pennies Mathematics, NCTM, 2000 Concept periodically. They can be grouped in piles of five or ten. NCTM Addenda Series – Kindergarten Money Early Childhood Math, ECM, Book 8. Place a coin in a sock. Children must identify the coin by putting their hand in the Peter and the Penny Tree PWC Grade Level Objective K.7 sock and feeling the coin. Twenty Six Letters and Ninety-Nine Cents Virginia SOL K.7 by Tana Holban Place a penny, nickel, dime, and quarter in a sock. Children must put their hand in I went to the Market by Joseph Domjan the sock, feeling the coins. The teacher calls out a coin and children take it out of the sock. AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Quick Quilts Part 1 and 2,‖ AIMS Magazine, Volume 7 Issue 8 ―A Pig's Tale,‖ AIMS Magazine, Volume 7 Issue 10 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Measurement What types of instruments are used to measure time? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How are clocks and calendars used to measure time? to: Measurement and Geometry Identify different types of clocks (analog Critical Attributes and digital) as instruments to measure Concept Many experiences in measuring physical objects, using nonstandard and standard units time. Time of measurement, help to develop initial understanding of measurement and will help Identify the components of a calendar, students connect a tool with its purpose in measuring. including days, months, and seasons. PWC Grade Level Objective K.8 Tell time on an analog clock to the hour. K.8A The student will identify Selecting from among various measuring instruments and determining which can be Tell time on a digital clock to the calendars and clocks as instruments used to solve various real-life problems is introduced at this level. hour. used to measure time; and hours and days as units of time. A precursor to connecting tools to a type of measure is an introduction to the concepts Essential Understanding K.8B The student will tell time to of length, weight, time, and temperature. All students should: the hour using an analog or digital Identify an appropriate measuring tool for a clock. Many experiences in relating time on the hour to daily routines and school schedules given unit of measure. (e.g., catching the bus, lunch, recess, and resource time) help students develop Apply an appropriate technique, depending Virginia SOL K.8 personal referents for time. on the type of clock, to determine time to The student will identify the the nearest hour. instruments used to measure length Making sense of telling time to the nearest hour is reinforced when students recognize (ruler), weight (scale), time (clock: the positions of the hands on an analog clock and identify the corresponding time to digital and analog; calendar: day, the hour. month, and season), and temperature (thermometer). Virginia SOL K.9 The student will tell time to the hour using an analog or digital clock. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Each student moves the hands on his/her clock to show the hour indicated by the PWC Math Web Page: Measurement number of "chimes‖ heard. Next, the students show one hour before the hour and http://www.pwcsmath.com one-hour after the hour. Curriculum and Evaluation Standards, SOL Reporting Category NCTM, 1989 Measurement and Geometry The students take turns showing the time by placing numbers on a teacher-made Principals and Standards for School digital clock. Next, the students use number squares on their own digital clock to Mathematics, NCTM, 2000 Concept show times that match the hands positioned by their partner on an analog clock. NCTM Addenda Series – Kindergarten Time Early Childhood Math, ECM, Book 7 Students work in groups. Each group is given a clock face and a set of number Today is Monday by Eric Carle PWC Grade Level Objective K.8 cards 1-12. Students identify the missing numbers on the clock face and put the What Time Is It Around the World by Virginia SOL K.8 correct number cards in place. When each group is finished, they will move to the Hans Baumann next clock. Explorations I, Chapter 10 Chicken Soup with Rice by Maurice Students examine calendars to discuss its organization into months and days. Then Sendak further discuss the months in relation to seasons. Clocks and How They Go by Gail Gibbons Record: Learning Basic Skills Through Music, Volume Two Paper Clocks by Hap Palmer AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Measurement What type of instrument is used to measure length? mathematical communication, mathematical reasoning, connections, and SOL Reporting Category How is a ruler used to solve real-life problems when measuring? representation to: Measurement and Geometry Compare and describe lengths Concept What is non-standard measurement? (shorter or longer) of two objects, Linear Measurement using direct comparison and How are two objects measured and compared? nonstandard units of measure, e.g., PWC Grade Level Objective K.9 foot length, hand span, new pencil, K.9A The student will identify and Critical Attributes paper clip, block. recognize various instruments used to Many experiences in measuring physical objects, using nonstandard and standard units Compare and describe heights (taller or measure length (ruler) and explore the use of measurement, help to develop initial understanding of measurement and will help shorter) of two objects, using direct of various instruments for customary and students connect a tool with its purpose in measuring. comparison and nonstandard units of non-standard measurement. measure, e.g., book, hand span, new K.9B The student will compare two objects Selecting from among various measuring instruments and determining which can be pencil, paper clip, and block. or events, using direct comparisons or used to solve various real-life problems is introduced at this level. Identify a ruler as an instrument to nonstandard units of measure, according to measure length. the following attributes: length (longer, A precursor to connecting tools to a type of measure is an introduction to the concepts shorter), and height (taller, shorter). of length, weight, time, and temperature. Essential Understanding All students should: Virginia SOL K.8 Length is the distance along a line or figure from one point to another. Height is the Identify an appropriate measuring tool The student will identify the instruments vertical length of a perpendicular to its base. for a given unit. used to measure length (ruler), weight Compare and order objects according to (scale), time (clock: digital and analog; calendar: day, month, and season), and Extensive opportunities are needed to gain the ability to compare the attributes of their attributes. temperature (thermometer). objects. Develop an understanding of measuring with nonstandard and standard units. Virginia SOL K.10 Objects are measured using standard and non-standard measurement tools. Standard The student will compare two objects or events, tools used to measure length are a ruler and a yardstick. using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hands span, new pencil, paper clip, block, etc. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand The teacher reads Peter's Chair and will have two different size chairs PWC Math Web Page: Measurement available. One is Peter's "old" chair and one is his "grown-up" chair. The http://www.pwcsmath.com students measure from floor to seat of each chair and compare their heights. Early Childhood Math, ECM, Books 3 SOL Reporting Category and 7. Measurement and Geometry Students make clay snakes and compare lengths. Curriculum and Evaluation Standards, NCTM, 1989 Concept Allow each child to construct a train using connecting cubes. After each child Principals and Standards for School Linear Measurement has constructed their train, he or she will look around to find objects that are Mathematics, NCTM, 2000 shorter or longer than their train. Allow time for discussion about how they NCTM Addenda Series – Kindergarten PWC Grade Level Objective K.9 found longer or shorter objects. Developing Number Concepts: Virginia SOL K.8 Counting Comparing and Pattern Virginia SOL K.10 The child will trace their foot and cut it out. He or she will explore the room to Chapter 3 find something that is as long as his/her foot. Allow time for discussion about Connect to the NCTM Standards K their findings. pp 94-119 AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Wrap Around Ruler,‖ AIMS Magazine, Volume 11 Issue 10 ―How Tall Are You,‖ Fall Into Math and Science ―Feet Findings,‖ Spring Into Math and Science ―Look At Me Now,‖ AIMS Magazine, Volume 9 Issue 2 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Measurement What type of instrument is used to measure weight? mathematical communication, mathematical reasoning, connections, and representations SOL Reporting Category How is a scale used to solve real-life problems when measuring? to: Measurement and Geometry Identify different types of scales as How are two objects measured and compared? instruments to measure weight. Concept Compare and describe weights (heavier or Weight Critical Attributes lighter) of two objects, using direct Measurement at the kindergarten level will focus on the direct comparison of two comparison and nonstandard units of PWC Grade Level Objective K.10 objects or the measurement of the objects with nonstandard units of measurement measure, e.g., book, cubes, new pencil, K.10A The student will identify (hand, thumb, pencil, etc). paper clip, and block. and recognize various instruments used to measure weight (scale). Many experiences in measuring physical objects, using nonstandard and standard units Essential Understanding K.10B The student will compare of measurement, help to develop initial understanding of measurement and will help All students should: two objects or events, using direct students connect a tool with its purpose in measuring. Identify an appropriate measuring tool for a comparisons or nonstandard units Selecting from among various measuring instruments and determining which can be given unit of measure. of weight (heavier, lighter). used to solve various real-life problems is introduced at this level. Compare and order objects according to their attributes. Virginia SOL K.8 A precursor to connecting tools to a type of measure is an introduction to the concepts Develop an understanding of measuring The student will identify the of length, weight, time, and temperature. with nonstandard and standard units of instruments used to measure length measure. (ruler), weight (scale), time (clock: Weight is a measure of the heaviness of object. digital and analog; calendar: day, month, and season), and temperature Objects are measured using standard and non-standard measurement tools. Standard (thermometer). tools used to measure weight are different types of scales. Virginia SOL K.10 Extensive opportunities are needed to gain the ability to compare the attributes of The student will compare two objects or objects. events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hands span, new pencil, paper clip, block, etc. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand The students make a hanging balance from margarine tubs and a plastic clothes PWC Math Web Page: Measurement hanger to be used to weigh objects. http://www.pwcsmath.com Curriculum and Evaluation Standards, SOL Reporting Category The teacher will have rulers, scales, clocks, and thermometers available for use NCTM, 1989 Measurement and Geometry and experimentation by students. Principals and Standards for School Mathematics, NCTM, 2000 Concept Students compare the weight of two objects using plastic grocery bags. Hold one NCTM Addenda Series – Kindergarten Weight bag containing an object in one hand and a bag containing the other object in the Early Childhood Math, ECM, Books 3 other hand. and 7 PWC Grade Level Objective K.10 Math Their Way Virginia SOL K.8 Developing Number Concepts: Virginia SOL K.10 Counting Comparing and Pattern, Chapter 3 Connect to the NCTM Standards K, p102-107 Math Their Way Summary Newsletter. AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―A Pumpkin With Class,‖ AIMS Magazine, Issue 3 ―Whoa -That's Heavy,‖ Glide Into Winter ―Let Me Count The Ways,‖ Primarily Bears Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Measurement What type of instrument is used to measure temperature? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How is a thermometer used to solve real-life problems when measuring? to: Measurement and Geometry Identify different types of thermometers as What is non-standard measurement? instruments used to measure temperature. Concept Be introduced to the different types of Temperature How are two objects measured and compared? thermometers and their uses. Compare and describe temperatures PWC Grade Level Objective K.11 Critical Attributes (hotter or colder) of two objects or events, K.11A The student will identify Many experiences in measuring physical objects, using nonstandard and standard units using direct comparison. and recognize various instruments of measurement, help to develop initial understanding of measurement and will help used to measure temperature. students connect a tool with its purpose in measuring. Selecting from among various Essential Understanding K.11B The student will compare measuring instruments and determining which can be used to solve various real-life All students should: two objects or events, using direct problems is introduced at this level. Identify an appropriate measuring tool for a comparisons or nonstandard units given unit. of temperature. A precursor to connecting tools to a type of measure is an introduction to the concepts Compare and order objects according to of length, weight, time, and temperature. their attributes. Virginia SOL K.8 Develop an understanding of measuring The student will identify the Temperature is the degree of hotness or coldness of a body or environment. Students with nonstandard and standard units. instruments used to measure length should make comparisons telling whether something is hotter/colder than something (ruler), weight (scale), time (clock: else. digital and analog; calendar: day, month, and season), and Objects are measured using standard and non-standard measurement tools. A standard temperature (thermometer). tool used to measure temperature is a thermometer. Virginia SOL K.10 Thermometers can be circular, bar or digital. The student will compare two objects or events, using direct comparisons or Extensive opportunities are needed to gain the ability to compare the attributes of nonstandard units of measure, according objects. to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hands span, new pencil, paper clip, block, etc. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Introduce each of the measuring instruments throughout the year as they relate to PWC Math Web Page: Measurement a unit of study. Discuss their uses (a thermometer measures temperature - body, http://www.pwcsmath.com air) and provide opportunities for students to have hands-on use of the instrument Curriculum and Evaluation Standards, SOL Reporting Category (keep a temperature graph for a week). Discuss results. NCTM, 1989 Measurement and Geometry Principals and Standards for School The teacher will have thermometers available for use and experimentation by Mathematics, NCTM, 2000 Concept students. NCTM Addenda Series – Kindergarten Temperature Early Childhood Math, ECM, Book 7 Explorations I, Chapter 10 PWC Grade Level Objective K.11 Chicken Soup with Rice by Maurice Virginia SOL K.8 Sendak Virginia SOL K.10 AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―What is the Temperature?‖ Primarily Physics . Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Geometry How are circles, squares, triangles, and rectangles recognized and created? mathematical communication, mathematical reasoning, connections, and representation to: SOL Reporting Category How are two geometric shapes the same or different? Identify a circle, square, triangle, and Measurement and Geometry rectangle. Concept What shapes are seen in the classroom, on the playground, and at home? Describe properties of triangles, squares, and Plane Figures rectangles, including number of sides and Critical Attributes number of corners. PWC Grade Level Objective K.12 A square is a rectangle with all four sides having the same length. Create a circle, triangle, square, and K.12A The student will identify, describe, A rectangle is a quadrilateral with four right angles. rectangle using various methods (i.e. body and draw two dimensional plane geometric A quadrilateral is a polygon with four sides. movements, geoboards, tactile materials, figures (circle, triangle, square, and A triangle is a polygon with three angles and three sides. Children should be shown etc.). rectangle). different types of triangles such as equilateral, isosceles, scalene, right, acute and Describe a circle. K.12B The student will describe the location obtuse. However, they are not expected to name the various types. Draw a circle, square, triangle, and of one object relative to another (above, below, and next to) and identify rectangle. representations of plane geometric figures Presentation of triangles, rectangles, and squares should be made in a variety of spatial Identify pictorial representations of a circle, (circle, triangle, square, and rectangle) orientations so that students do not develop the common misconception that triangles, square, triangle, and rectangle, regardless of regardless of their position and orientation in rectangles, and squares must have one side parallel to the bottom of the page it is their position and orientation in space. space. printed on. Describe the location of one object relative K.12C The student will compare the size to another using the terms above, below, and (larger/smaller) and the shape of plane A circle is a closed curve with all points in one plane and the same distance from a next to. geometric figures (circle, triangle, square, fixed point (the center). Compare and group geometric figures and rectangle). according to their size (larger/smaller). A plane geometric figure is any two-dimensional closed shape. Circles and polygons Compare and group geometric figures Virginia SOL K.11 The student will identify, describe, and draw are examples of plane geometric figures. (circle, square, triangle, and rectangle) two-dimensional (plane) geometric figures Representations of a circle, square, rectangle, and triangle can be found in the child’s according to their shape. (circle, triangle, square, and rectangle. environment (e.g., school/home), and students should have opportunities to Virginia SOL K.12 identify/classify things in their environment by the type of shape it represents. Essential Understanding The student will describe the location of one All students should: object relative to another (above, below, and Children are often confused when a shape such as a square is rotated. They frequently Use their knowledge of two-dimensional next to) and identify representations of plane refer to the rotated square as a diamond. Clarification needs to be ongoing – a square is figures to help them systematically represent geometric figures (circle, triangle, square, a square regardless of its orientation. There is no such geometric shape as a diamond. and describe their world. and rectangle) regardless of their position and Develop an understanding of the shapes of orientation in space. Virginia SOL K.13 geometric figures by using various methods. The student will compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle). continued continued Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Critical Attributes Continued Continued Geometry An important part of the geometry strand in grades K-2 is the naming and describing Essential Understanding SOL Reporting Category of shapes. Children move from their own vocabulary and begin to incorporate All students should: Measurement and Geometry conventional terminology as the teacher uses the geometric terms. The van Hiele Use a variety of skills that relate to Concept theory of geometric understanding describes how students learn geometry and direction, distance, and position in space to Plane Figures provides a framework for structuring student experiences that should lead to enhance their navigation skills. conceptual growth and understanding. Develop strategies to sort and/to group PWC Grade Level Objective K.12 Level 0: Pre-recognition plane geometric figures and begin to refine K.12A The student will identify, describe, Geometric figures are not recognized. For example, students cannot differentiate the vocabulary used to explain their and draw two dimensional plane geometric between three-sided and four sided polygons. strategies. figures (circle, triangle, square, and Level 1: Visualization rectangle). Geometric figures are recognized as entities, without real awareness of parts of K.12B The student will describe the location of one object relative to another (above, relationships between components of the figure. A student should recognize and name below, and next to) and identify figures, and distinguish a given figure from others that look somewhat the same. ―I representations of plane geometric figures know it’s a rectangle because it looks like a door, and I know that the door is a (circle, triangle, square, and rectangle) rectangle.‖ regardless of their position and orientation in Level 2: Analysis space.. Properties are perceived but are isolated and unrelated. A student should recognize K.12C The student will compare the size and name properties of geometric figures. ―I know it’s a rectangle because it is closed, (larger/smaller) and the shape of plane it has 4 sides and 4 right angles.‖ geometric figures (circle, triangle, square, and rectangle). Early experiences with comparing and sorting shapes assist students in analyzing the Virginia SOL K.11 characteristics and properties of two-dimensional geometric shapes. Attribute blocks, The student will identify, describe, and make relational attribute blocks, and Tangrams are among the manipulatives that are plane geometric figures (circle, triangle, particularly appropriate for sorting and comparing use. square, and rectangle). Virginia SOL K.12 The student will describe the location of one object relative to another (above, below, and next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their position and orientation in space. Virginia SOL K.13 The student will compare the size (larger/smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle). Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Geometric manipulatives which can be used to combine plane geometric figures PWC Math Web Page: Geometry to create familiar shapes are: http://www.pwcsmath.com - Tangrams - Attribute blocks Curriculum and Evaluation Standards, SOL Reporting Category - Pattern blocks - Power blocks NCTM, 1989 Measurement and Geometry Principals and Standards for School Place shapes on an overhead projector and move the projector closer and further Mathematics, NCTM, 2000 Concept from the screen. Predict and discuss what happens to the shape. NCTM Addenda Series – Kindergarten Plane Figures Geometry and Spatial Sense, NCTM Provide construction paper cut into different shapes. Students create pictures from Addenda Series - Kindergarten PWC Grade Level Objective K.12 the combination of shapes. Early Childhood Math, ECM, Book 3 Virginia SOL K.11 Math Their Way Virginia SOL K.12 Students will arrange their bodies on the floor to make shapes. Connect to the NCTM Standards K Virginia SOL K.13 pp 94 -119 How many steps do you take on each side as you walk around the shape? How Math Their Way Summary Newsletter many corners do you meet? Shapes and Things by Tana Hoban Red Bear's Fun with Shapes by Bodel Put shapes in a bag. Students will identify the different shapes by touch. Rikys Tatum's Favorite Shape by Dorothy Thole Look at a shape; student will find an object in the classroom with that shape. Round Is a Pancake by Joan Sullivan Discuss similarity and differences. Circles, Triangles, and Squares by Tana Hoban Play a fishing game. The teacher will provide a variety of circles, squares, Shapes by Jan Pienkowski triangles, and rectangles with a paper clip on each and a "rod" with a magnet "hook". Each student takes turns fishing for a shape and identifying the shape AIMS Activities: caught. Virginia SOL Correlations to AIMS Activities: Groups of students are provided with a variety of shapes in varying colors and http://www.aimsedu.org/statedocs/virginia/ sizes and each responsible for creating a "shape land". virginia.html ―You Drive Me Crackers,‖ Fall Into Math Play "I Spy". Students guess what item in the room is being described as the and Science teacher provides the item's shape and other clues such as "I spy a square that lets ―Shape Up,‖ Fall Into Math and Science us see outside". ―Shape Search,‖ Sense-able Science ―Shape Takers,‖ AIMS Magazine, Volume 11 Issue 3 ―Busy with Buses,‖ AIMS Magazine, Volume 10 Issue 6 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Geometry How are spheres, cubes, and cylinders identified? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category What are the characteristics of a sphere, cube, and cylinder? to: Measurement and Geometry Name and describe a sphere, cube, and Critical Attributes cylinder Concept Spheres, cubes, and cylinders can be identified by the number and size of their edges Find 3-dimensional shapes in the Solid Figures and corners and the shape and number of their faces. classroom. Sort objects according to their shape. PWC Grade Level Objective K.13 A sphere has no faces, edges, or corners. Compare and group geometric figures The student will identify, describe, sort, according to size (i.e. larger/smaller). and manipulate three-dimensional A cylinder has two circular faces, and no edges or corners. Compare and describe similarities and models of geometric figures (sphere, differences between groups of three cube, and cylinder). A cube has 6 faces, 12 edges, and 8 corners. dimensional geometric figures. No SOL Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Have students bring in real objects from home that are a sphere, cube, or cylinder. PWC Math Web Page: Geometry Sort by shape and talk about what was shared. http://www.pwcsmath.com Curriculum and Evaluation Standards, SOL Reporting Category Play "I Spy.‖ Students guess what item in the room is being described as the NCTM, 1989 Measurement and Geometry teacher provides the item's shape and other clues such as "I spy a square that lets Principals and Standards for School us see outside". Mathematics, NCTM, 2000 Concept NCTM Addenda Series – Kindergarten Solid Figures Sort shapes using a Venn Diagram. Geometry and Spatial Sense, NCTM Addenda Series - Kindergarten PWC Grade Level Objective K.13 Early Childhood Math, ECM, Book 2, 3, 7 No SOL Math Their Way Math Their Way Summary Newsletter. Shapes and Things by Tana Hoban Brown Rabbit's Shape Book by Alan Baker Red Bear's Fun with Shapes by Bodel Rikys Tatum's Favorite Shape by Dorothy Thole The Shapes Game by Paul Rogers AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―You Drive Me Crackers,‖ Fall Into Math and Science ―Shape Up,‖ Fall Into Math and Science Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Probability and Statistics What methods can be used to gather and record data? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How is data sorted and classified? to: Probability and Statistics Gather data on given categories by Critical Attributes counting and tallying e.g., favorites, Concept Data is information collected about people or things. The primary purpose of number of days of various types of weather Statistics collecting data is to answer questions. during a given month, types of pets, types of shoes. PWC Grade Level Objective K.14 Tallying is a method for gathering information. Tally marks are used to show how The student will gather data relating to often something happens or occurs. Each tally mark represents one occurrence. Tally Essential Understanding familiar experiences by counting, marks are clustered into groups of five, where there are four slash marks representing All students should: tallying, sorting, and classifying. the first four occurrences and the fifth slash mark crosses the first four on a diagonal to Pose questions and gather data about represent the fifth occurrence. themselves and their surroundings. Virginia SOL K.14 Understand how data are collected and The student will gather data relating to When data are presented in an organized manner, children can describe the results of presented in an organized manner by familiar experiences by counting and their investigation, e.g., identify parts of the data that have special characteristics, counting and tallying. tallying. including categories with the greatest, the least, or the same. In the process of gathering data, students make decisions about what is relevant to their investigation, e.g., students collecting data on their classmate’s favorite pets decide to limit the categories to common pets. When students begin to collect data, they recognize the need to categorize, which helps develop the understanding of ―things that go together.‖ Categorical data is used when constructing picture graphs and bar graphs. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Encourage students to gather graph information as they are constructing graphs PWC Math Web Page: Probability and Statistics (concrete, pictorial, symbolic). Then ask "Can you make predictions or draw any http://www.pwcsmath.com conclusions from the graph?" Record response on large chart paper. Curriculum and Evaluation Standards, SOL Reporting Category NCTM, 1989 Probability and Statistics Using birthday cake cut-outs, make tally marks (to represent candles) for each Principals and Standards for School child who has a birthday in a specific month. Mathematics, NCTM, 2000 Concept NCTM Addenda Series – Kindergarten Statistics The students are divided into two teams and play any game where a correct Early Childhood Math, ECM, Books 1 response earns a point. Tally the points by counting. and 6 PWC Grade Level Objective K.14 Math Their Way, p. 140-163 Virginia SOL K.14 The teacher provides tallying activities in daily lessons by tallying and counting Math Their Way Summary Newsletter such things as, number of boys and girls present, birthdays in the month, type of Connect to the NCTM Standards K, milk, or ice cream for snack. pp 122-127 Jeanne Marie Counts Her Sheep by Françoise The Twelve Days of Christmas North by Lois Barger The Mitten by Jan Brett Caps For Sale by Esphyr Slobodkina AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Probability and Statistics What does the data on a graph show? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How can data be shown in different ways? to: Probability and Statistics Display data by arranging concrete objects Critical Attributes into organized groups to form a simple Concept Pictorial graphs are graphs that use pictures to show and compare information. A key object graph. Statistics is often used to indicate what each picture represents e.g., one picture of a dog Display data using pictorial representations represents five dogs. of the data to form a simple pictorial graph, PWC Grade Level Objective K.15 (e.g., picture graph of the types of shoes Virginia SOL K.15 Object graphs are graphs where concrete materials are used to represent the worn by students on a given day). The student will display objects and categorical data that is collected e.g., cubes stacked by the month, where one cube Display information in tables, either in information, using object and pictorial represents the birthday month of each student. rows or columns, (e.g., tables showing the graphs and tables. number of bunnies in one column and the Tables are an orderly arrangement of data in which the data are arranged in columns number of ears the bunnies have in another, and rows in an essentially rectangular format. Tables may be used to display some or the time schedule for classroom type of numerical relationship or organized lists e.g., input/output functions; tables activities). showing one candy costs five cents, two candies cost ten cents, etc. Essential Understanding Students represent data to convey results at a glance, using concrete objects, pictures, All students should: and numbers to give a ―picture‖ of the organized data. Understand data can be represented using concrete objects, pictures, and graphs. When data are displayed in an organized manner, children can describe the results of Understand that different types of their investigation. representations emphasize different things about the same data. Graphs can be used to make connections between mathematics and social studies Understand pictorial graphs use pictures to and/or science, e.g., job areas and the different people that work in these areas: show and compare information; object health—doctor, nurse; education—teachers, principals, students, parents. graphs use concrete materials to represent categorical; and tables can be used to show an orderly arrangement of data in columns and rows. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Students build concrete graphs with bodies, shoes, and toys. PWC Math Web Page: Probability and Statistics http://www.pwcsmath.com Student place pictures on a graph in place of the real object. Early Childhood Math, ECM SOL Reporting Category Curriculum and Evaluation Standards, Probability and Statistics The student builds a symbolic graph. In place of the real object, the student writes NCTM, 1989 a name or word on the graph. Principals and Standards for School Concept Mathematics, NCTM, 2000 Statistics Use descriptive vocabulary to interpret data: more, less, equal, fewest, etc. NCTM Addenda Series – Kindergarten Connect to the NCTM Standards K,, PWC Grade Level Objective K.15 Graph construction begins with two columns and extends to several. pp 128 -133 Virginia SOL K.15 Caps for Sale by Esphyr Slobodkina A variety of graphs need to be constructed (horizontal, vertical, and pie). Using a Explorations for Early Childhood, teacher-made grid, children will color a post-it-note or ice cream shape to show Chapters 7 and 16 their favorite flavor and then place on a classroom grid. Repeat activity using Guess Who My Favorite Person Is? by story characters, eye color, etc. Byrd Baylor Whose Shoes? By Brian Wildsmith Red Is Best by Kathy Stinson AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Gingerbread Kids,‖ AIMS Magazine, Volume 6 Issue 5 ―Thanksgiving Soup,‖ AIMS Magazine, Volume 6 Issue 4 ―Pets are Part of the Picture,‖ AIMS Magazine, Volume 5 Issue 10 ―Pockets,‖ AIMS Magazine, Volume 10 Issue 2 ―Going Nuts,‖ Fall Into Math and Science ―Valentine Candy Count,‖ Fall Into Math and Science Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Probability and Statistics Which color will occur most frequently when a two-color counter is dropped or a mathematical communication, mathematical multi-colored spinner is used? reasoning, connections, and representation SOL Reporting Category to: Probability and Statistics How can the results of a probability experiment be recorded? Conduct investigations of probability through hands-on activities e.g., dropping Concept What can be predicted from a probability experiment? two-colored counters or using a multi- Probability colored spinner. Critical Attributes Describe verbally, pictorially and/or with PWC Grade Level Objective K.16 Probability is the likelihood that an event will occur. tally marks the outcome of dropping a two- Virginia SOL K.16 colored counter or using a multicolored The student will investigate and describe The concept of experimental probability is introduced through informal activities such spinner e.g., the number of times the red the results of dropping a two-colored as dropping a two-colored counter (usually a chip that has a different color on each side of the counter landed up compared to counter or using a multicolored spinner. side) or using a multicolored spinner (a circular spinner that is divided equally into the number of times the counter was two, three, four, or more equal ―pie‖ parts where each part is filled with a different dropped. color). Essential Understanding Answering questions about the likelihood of events, such as, ―Which is more likely (or All students should: less likely)?‖, begin at this level. Hands-on experimentation with two-colored counters Develop an understanding of chance and spinners help children to understand the likelihood of an event. (likelihood of an event through informal investigations with spinners and two- Early probability investigations help students learn to enjoy and appreciate the value colored counters). of probability. Through discussion, students may realize that a particular outcome is dependent upon the given situation. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand In small groups, drop a two-color counter ten times. Discuss which side (color) PWC Math Web Page: Probability and Statistics shows up more. Discuss results. Repeat again and see if results change. (Drop http://www.pwcsmath.com five times and see if results are the same). Through exploration and discussion, Curriculum and Evaluation Standards, SOL Reporting Category students can begin to make predictions. NCTM, 1989 Probability and Statistics Principals and Standards for School Use Unifix blocks. Each time a student spins the multi-colored spinner, he/she Mathematics, NCTM, 2000 Concept places a unifix block of the same color in the middle of the table. After spinning a NCTM Addenda Series – Kindergarten Probability given number of times, count the blocks to see what color the student has most of Mathematics Their Way Summary Newsletter PWC Grade Level Objective K.16 Place colored blocks in a bag (i.e., 10 of one color and 10 of another color). Math Their Way, Chapter 4 Virginia SOL K.16 Students predict what color block will be selected from the bag. Select one block Connect to the NCTM Standards K, from bag without peeking. Graph results. Next, the teacher will ask if this will be pp 134-139 the result every time. Continue activity a given number of times. AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Scatterbeans,‖ AIMS Magazine, Volume 10 Issue 4 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Patterns, Functions, and Algebra How are the color, size, shape, and texture of an object described? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How many different ways can these objects be sorted using one or more common to: Patterns, Functions, and Algebra attributes? Sort objects into appropriate groups (categories) based upon an attribute such as Concept How can data be gathered using concrete objects? size, shape, or color. Classification Classify sets of objects into three groups Critical Attributes (categories) of one attribute, e.g., for size: PWC Grade Level Objective K.17 To classify is to arrange or organize a set of materials according to a category or small, medium and large. The student will sort and classify objects attribute (a quality or characteristic of a thing). according to similar attributes (size, Essential Understanding shape, color, and texture). General similarities and differences among items are easily observed, and children All students should: entering kindergarten are able to focus on any one attribute. The teacher’s task is to Understand the same set of objects can be Virginia SOL K.17 move students toward a more sophisticated understanding of classification where two sorted and classified in different ways. The student will sort and classify objects or more attributes connect or differentiate sets such as those found in nature, e.g., according to similar attributes (size, leaves with different colors and different shapes. shape, and color). Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Compare two objects and tell how they are alike and different. (Venn Diagram) PWC Math Web Page: Patterns, Functions, and Algebra http://www.pwcsmath.com Provide a group of objects for students to search for common attributes. The Curriculum and Evaluation Standards, SOL Reporting Category teacher records the attributes and students sort objects according to those NCTM, 1989 Patterns, Functions, and Algebra attributes. Begin classifying using one attribute and extend to include many. Principals and Standards for School Mathematics, NCTM, 2000 Concept On the floor, make a circle of paper plates and place a colored piece of paper on NCTM Addenda Series – Kindergarten Classification each. As music plays, the students walk around the circle. When the music stops, Making Sense of Data, NCTM Addenda they stop next to the nearest plate. They name something in the room that is the Series - Kindergarte PWC Grade Level Objective K.17 same color as their plate. As an extension, colored paper can be exchanged with Early Childhood Math, ECM, Book 6 Virginia SOL K.17 objects such as shapes or picture cards. Math Their Way, p. 140-163 Connect to the NCTM Standards K, Students will sort their favorite books by different attributes. pp 140-145 Math Their Way Summary Newsletter The teacher demonstrates sorting a few attribute blocks into two groups, placing All Sorts Well, Tony them onto a piece of white or black construction paper, without explaining the The Button Box by Margarette Reid sorting rule. She then holds up one shape at a time, waiting for students to show A House Is A House For Me by Mary Ann her which group it fits into by silently holding up a white or black cube. When all Hoberman shapes have been sorted, the sorting rule is discussed. Is It Red? Is It Yellow? Is It Blue? by Tana Hoban Provide two boxes: one with the word NOT on it. Children sort objects into the Is It Rough? Is It Smooth? Is It Shiny? by boxes according to if they have the characteristic given or NOT. Tana Hoban Buttons, Buttons by Rozanne Lanczak Using two boxes, one labeled ―not,‖ students sort objects into those having a Williams certain characteristic and those that do ―not‖ have that characteristic. AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Harriet's Halloween Treats,‖ AIMS Magazine, Volume 6 Issue 5 ―If the Shoe Fits,‖ Glide into Winter ―Gingerbread Kids,‖ AIMS Magazine, Volume 6 Issue 5 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Objective Essential Questions Essential Skills and Processes Critical Attributes PWC Curriculum Strand Essential Questions The student will use problem solving, Patterns, Functions, and Algebra What is a pattern? mathematical communication, mathematical reasoning, connections, and representation SOL Reporting Category How is a pattern identified, created, and extended? to: Patterns, Functions, and Algebra Observe and identify the basic repetitive Critical Attributes pattern found in repeating patterns of Concept Pattern recognition is a fundamental cornerstone of mathematics, particularly algebra. common objects, sounds, and movements Patterns and Functions that occur in real-life situations, where A pattern is a series of objects, events, numbers or ideas that repeat or grow so that there are four or fewer elements in the basic PWC Grade Level Objective K.18 what comes next can be predicted. Movements, sounds, as well as objects can form a repetitive pattern, e.g., ABCD, AABB, K.18A The student will identify, and pattern. ABAB. describe patterns found in common Describe the basic repetitive pattern found objects, sounds, and movements. Extending patterns requires the following sequence: in a repeating pattern where there are four K.18B The student will extend a Identify the repeating function of the pattern. or fewer elements in the basic repetitive repeating pattern found in common Recreate the repeating function of the pattern. pattern, e.g., ABCD, AABB, ABAB. objects, sounds, and movements. Extend the repeating function of the pattern. Extend a repeating pattern by showing at least two repetitions, e.g., ABCDABCD; or Virginia SOL K.18 Pattern recognition and the extension of the pattern allows students to make AABBAABB. The student will identify, describe, and predictions. Identify patterns in the environment. extend a repeating relationship (pattern) found in common objects, sounds, and The simplest types of patterns are repeating patterns. The patterns can be oral, such as Essential Understanding movements. the refrain in Old MacDonald’s Farm — ―e-i-e-i-o‖; or physical with clapping and All students should: snapping patterns; or combinations of both with songs like the Hokey Pokey. In each Understand patterns are a way to recognize case, students need to identify the basic unit of the pattern and repeat it. Opportunities order and organize their world and to to create, recognize, describe, and extend repeating patterns are essential to the predict what comes next in an arrangement. primary school experience. Sample repeating patterns (repeating the basic unit): ABABABAB, ABCABC, AABBAABBAABB, AABAAB, AABCAABC, and ABACABAC. Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Curriculum Information Instructional Strategies Possible Suggested Activities Resources PWC Curriculum Strand Pattern Block Walls PWC Math Web Page: Patterns, Functions, and Algebra Make a pattern using 6 or 7 blocks. Then record the pattern. Extend the pattern http://www.pwcsmath.com using pattern blocks. Curriculum and Evaluation Standards, SOL Reporting Category NCTM, 1989 Patterns, Functions, and Algebra Use colored macaroni and have students make a necklace with patterns such as Principals and Standards for School ABAB, AABB, etc. Mathematics, NCTM, 2000 Concept NCTM Addenda Series – Kindergarten Patterns and Functions Students choose holiday cut-outs to color, cut, and glue onto sentence strips (or Early Childhood Math, ECM, Book 7 candy cane shape, etc.) to form a pattern. Math Their Way PWC Grade Level Objective K.18 Connect to the NCTM Standards K, Virginia SOL K.18 Using students, make people patterns, such as, boy-girl, boy-girl; tall-short, tall- pp 42-67 short; standing-kneeling, standing-kneeling, etc. Two, Four, Six, Eight (A Book About Legs) by Ethel and Leonard Kessler. Working in groups of three, the students take turns using two musical instruments The Most Amazing Hide and Seek Counting to create six sound patterns. Each student records the patterns in a Sound Pattern Book by Robert Crowther book. Groups exchange their books, taking turns to re-create the sound patterns by Brown Bear, Brown Bear by Bill reading the charts. Martin, Jr. Too Much Noise by Ann McGovern Going On a Bear Hunt The Little Drummer Boy by Ezra Keats AIMS Activities: Virginia SOL Correlations to AIMS Activities: http://www.aimsedu.org/statedocs/virginia/ virginia.html ―Pumpkin Cover-up,‖ AIMS Magazine, Volume 8 Issue 3 “A Jar That Likes to Keep You Guessing,‖ Primarily Bears, Book 1 Updated Jan. 10, 2006 Kindergarten Curriculum Map MAPPING FOR INSTRUCTION Teacher: _____________________________ School: _____________________________ Subject: Kindergarten Year: Revised 2005 Updated Jan. 10, 2006 Kindergarten Curriculum Map

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